Level measurement systems, i.e., for use in measuring the level of a material within a vessel, are well known. It is also known to locate the boundaries between different materials in a vessel by measuring the density of the vessel contents at different locations to form a density profile of the vessel and contents in order to identify density changes which are indicative of boundary regions. For example, it has been proposed in WO-A-00/22387 to measure the density profile of a medium by providing an axially distributed array of sources of ionising radiation, e.g. 241Am which is a source of low energy gamma radiation, to give collimated beams of said radiation and an axially distributed array of detectors disposed so that the medium under study extends between the sources and the detectors. By monitoring the radiation received by the detectors, the amount of radiation absorbed by the medium from each beam can be determined and so variations in the medium density can be detected. The system of WO-A-00/22387 employs linear arrays of sources and detectors which may extend to several meters in length when the system is intended for use in large vessels such as oil separators and storage vessels. In certain cases, such as high pressure applications or harsh environments, the level measurement system must be contained in a case of a minimum thickness and/or of a particular material. This can impose constraints on the type of radiation that may be used which in turn determines the type and amount of shielding and collimation required. A problem with forming such long source and detector arrays is that dense materials can be required to provide shielding and collimation of the sources and this results in a heavy instrument which is expensive and difficult to manufacture and manoeuvre. Also such long instruments may be prone to breakage during manufacture and installation. It is an object of the invention to provide a level measurement system that overcomes some, at least of the problems with the prior art systems.